Question

Solve the equation by completing the square. Round your solutions to the nearest hundredth if necessary. 7n^2 -14n-50=6

Answer 1

Given,

The expression is,

$7n^2-14n-50=6$

Required

The solution of the quadratic expression.

Taking the given expression as,

$\begin{gathered} 7n^2-14n-50=6 \\ 7n^2-14n-50-6=0 \\ 7n^2-14n-56=0 \\ 7(n^2-2n-8)=0 \\ n^2-2n-8=0 \\ n^2-2n+1-1-8=0 \\ n^2-2n+1=9 \\ (n-1)^2=9 \\ n-1=\pm3 \\ (Taking\text{ positive sign\rparen }n=-3+1=-2 \\ (Taking\text{ negative sign\rparen n= 3+1 =4} \end{gathered}$

Hence, the solution of the equation is -2 and 4.